AP Physics U1

Scalar Quantities

Can be fully described by magnitude

• MUST be positive

• EX: Distance and Displacment

Distance

Total length of an object’s path

• SCALAR

• CANNOT be negative

Speed

How fast an object is moving

• Scalar (MUST be positive)

• Distance/Time

Vector Quantities

Need to be described by both magnitude and direction

• CAN be negative OR positive

  • YOU determine what direction is positive and what direction is negative

• EX; Displacment and velocity

Displacment

Difference between object’s starting and ending posistion

• VECTOR

• Negative = one direction

• Posistion = another direction

Velocity

The rate at which an object’s posistion changes

• VECTOR

• AKA rate of displacment/times

Graphing over time displacment over time

• Rest: Flat line

• Change direction: The sign of the slope changes

• Fast: Steeper slope

• Slow: Smaller slope

Graphing over time velocity over time

• Rest: the line goes to y = 0 (meaning the displacment is NOT changing)

• Change direction: crosses the x-axis

• Fast: Larger magnitude (looking @ absolute value)

• Slow: Smaller magnitude (looking @ absolute value)

• NOTE: Can be also pretty blocky if there are just linear sections on the displacement v time graph)

Graphing over time acceleration over time

• Rest: WE DO NOT KNOW if an object is at rest UNLESS we know the initial velocity!

  • Zero acceleration does NOT mean at rest but means CONSTANT SPEED

• Change direction: WE DO NOT KNOW if an object is changing direction UNLESS we know velocity

  • When velocity crosses zero (looking at area under the curve (aka the area from the curve —> x axis) to look at total velocity which will tell you negative or postitive, negative meaning negative dircetion and posittive meaning posititve direction)

• Fast/Slow: WE CANT TELLL without knowing the sign of the velocity!

  • If velocity + accelration sign MATCH —> SPEEDING UP

  • If velocity + accelreation sign DO NOT MATCH —> SLOWING DOWN

• BASICALLY WE NEED TO KNOW THE VELOCITY!

  • If it crosses the x-axis we break it up, its now positive or negative vleocity

How to get velocity from acceleration curve

Accumulated area under the acceleration curve until that point PLUS the inital velocity

• YOU NEED to know the starting velocity

  • ex starting velcoity of 50 and then accumulated (from acceleration) is -10 would be final = 40

POSITIVE velocity means postitive direction

NEGATIVE velcotiy means negative direction

ACCELERATION ONLY TELLS YOU THE CHANGE!!

instantaneous veloicty v average velocity

Instantaneous velocity: the velocity at the time

• pin point the time and the velocity

average velocity:

• looking at the average

  • ex: looking at the area under the curve of the velocity v time graph (representng total/net displacment) and divide by total time

Displacment —> Velocity

Slope of displacment over time = velocity!

• Calculate it in chunks

Velocity —> Displamcent

Area under the curve of displamcent over time

Posistion —> velocity

Find the slope of the posistion-time graph

Velocity —> Acceleration

Find the slope of the velocity-time graph

Acceleration —> change in velocity

Find the area under the curve of the acceleration-time graph

Velocity —> Change in posistion/Displacment

Find the area under the curve of velocity-time graph

Object runing around (vlocity v time & displacment v time)

Positive velocity

the displacment slope is POSITIVE meaning the object is moving towards the positive side

• does NOT matter the origin only what direction we are headed

  • remember its VECTOR (can be positive OR negative)

Negative velocity

the displacment slope is NEGATIVE meaning the object is moving towards the NEGATIVE side

• does NOT matter the origin only what direction we are headed

  • remember its a VECTOR (can be positive OR negative)

Sign of velocity is soley dependent on

the slope of distance over time

• direction in relation to origin

Looking ONLY at velocity we don’t know…

• where it started

• where it ended

Acceleration

the rate of change of the object’s displacment

• AKA: The slope of velocity v time

  • velocity/time

• If the sign of acceleration and velocity match —> speeding up

• if the sign of acceleration and velocity dont match —> slowing down

• ONLY exists if the object’s velocity is NOT constant

• Posistion versus time graph must be curved to have a linear velocity v time and thus have acceleration

Linearization

changing the axes on a graph to force the data into a linear relationship

if (var 1) = (con)(var 2) is a TRUE equation graphing….

(var 1) over (var 2) will produce a line with slope (con)

• y = mx + b

y = mx+b

(var 1) = (con) (var 2)

—>

(vertical axsis) = (slope)(horizontal axis)

When can you use the kinematic equations

When acceleration is constant.

How do you choose a kinematic equation?

List your knowns and unknown. Choose an equation containing your knowns and only one unknown.

What is the basic process for solving a kinematics problem?

• List givens

• Choose + direction

• Identify unknown

• Choose equation

• Substitute

• Solve

• Check units/sign

V₀

nitial velocity: the object's velocity at the beginning of the time interval.

V_x

Velocity

a_x

acceleration

t

time

x

final posistion

x₀

inital posistion

how to solve free fall problems

treated like a kinematics problems but using acceleration = gravity

if up is positive what is accerlaation due to gravity

if down is positive what is acceleration due to gravity

up is postitive? acceleration is negative

down is posititve? acceleration is positive

What is the velocity at the highest point of an upward throw?

v = 0 momentariyly

At rest

velocity at 0

starts from rest

v_{0 =} 0

Stops

v = 0

Comes to a stop

v = 0

dropped/released

inital velocity = 0

thrown

the object has a nonzero inital velocity

accelerates

acceleration is non zero

free fall

GRAVITY!

Returns to starting point

displacment/x final - x inital = 0

X final - X inital

DISPLACMENT

if you dont have displacment

If you dont have final velocity (v_x)

if yu dont have acceleration (a_x)

Free fall

the motion of an object only under the influence of gravity

• all objects (free falling) fall at the same rate regardless of shape or mass

• NEGLECTING air resistance for analyzing the free falling objects

objects at a given location and in absence of aiar resistence in freee fall have the same constant acceleration (GRAVITY!)
- 9.81m/s²

1: speeding up (moving awar from 0) in positive direction

2: constant movmenet in postitive direction

• flat line = constant

• rest = 0

3: slowing down in positive direction

4: speeding up in the negative direction

5: slowing down in the negative diection

Direction of speeding up/slowing down is SOLEY dpendenant on the….

VELOCITY

• postitive velocity = postivie direction

• negative velocity = negative direction

NOT THE SLOPE! LEGIT JUST ABOVE THE X AXIS OR BELOW IT.

Linearization

1. Identify function that relates all your variables, most of the time from an euqation we know/derive (or sometimes through shape)

2. Manipulate the equation until it’s in the form (variable 1) = (constants)(variables 2)

3. Put (variable 1) on the vertical axis and (variable 2) on the horizontal axis

4. Make new column in data table corresponding to each new axis

5. Plot data on new axes- should produce line!

6. Draw line of best fit and find its slope using two points on the line (NOT real data points)

7. (usually) Solve for desired quantity from slope

How do directions work

The second thing always goes first

ex: NE —> north of east = east first and then north

Quadratic forumla